Journal of Mathematical Sciences

, Volume 213, Issue 4, pp 461–503 | Cite as

On the Resolvent of Multidimensional Operators with Frequently Alternating Boundary Conditions with the Robin Homogenized Condition

  • D. I. Borisov
  • T. F. Sharapov

We consider an elliptic operator in a multidimensional domain with frequent alternation of the Dirichlet condition and the Robin boundary condition in the case where the homogenized operator contains only the original Robin boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain order sharp estimates for the rate of convergence. We construct a complete asymptotic expansion for the resolvent in the case where the resolvent acts on sufficiently smooth functions and the alternation of boundary conditions is strictly periodic and is given on a multidimensional hyperplane. Bibliography: 23 titles.


Boundary Layer Asymptotic Expansion Solvability Condition Robin Boundary Condition Internal Expansion 
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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Mathematics, USC RASUfaRussia
  2. 2.Bashkir State Pedagogical UniversityUfaRussia
  3. 3.University of Hradec KrálovéHradec KrálovéCzech Republic

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